
"""simple docstring"""


def 						lowerCamelCase__      (				UpperCAmelCase_ = 1_00_00_00					)->				int:







       """simple docstring"""
       UpperCamelCase       			=		limit + 1
       UpperCamelCase       			=		[0] * limit
       for first_term in range(1		,   UpperCAmelCase_					):
              for n in range(UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_					):
                     UpperCamelCase       			=		first_term + n / first_term
                     if common_difference % 4:  # d must be divisble by 4
                            continue
                     else:
                            common_difference /= 4
                            if (
                                first_term > common_difference
                                and first_term < 4 * common_difference
                            ):  # since x,y,z are positive integers
                                   frequency[n] += 1  # so z>0 and a>d ,also 4d<a

       UpperCamelCase       			=		sum(1 for x in frequency[1:limit] if x == 10					)

       return count


if __name__ == "__main__":
      print(F'''{solution() = }''')







"""simple docstring"""


def 						lowerCamelCase__      (				UpperCAmelCase_ = 60_08_51_47_51_43					)->				int:







       """simple docstring"""

       try:
              UpperCamelCase       			=		int(UpperCAmelCase_					)
       except (TypeError, ValueError):
              raise TypeError("Parameter n must be int or castable to int."					)
       if n <= 0:
              raise ValueError("Parameter n must be greater than or equal to one."					)
       UpperCamelCase       			=		2
       UpperCamelCase       			=		0
       if n == 2:
              return 2
       while n > 2:
              while n % i != 0:
                     i += 1
              UpperCamelCase       			=		i
              while n % i == 0:
                     UpperCamelCase       			=		n // i
              i += 1
       return int(UpperCAmelCase_					)


if __name__ == "__main__":
      print(F'''{solution() = }''')





